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Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Formula

GoEfficiency of Screw Jack when only Screw Friction is Considered Formula

GoMaximum Efficiency of Screw Jack Formula

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The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power. Check FAQs

η = \frac{W \cdot \tan (ψ) \cdot d}{W l \cdot \tan (ψ + Φ) \cdot d + μ c \cdot W l \cdot R c}

η - Efficiency?W - Weight?ψ - Helix Angle?d - Mean Diameter of Screw?W_l - Load?Φ - Limiting Angle of Friction?μ_c - Coefficient of Friction For Collar?R_c - Mean Radius of Collar?

Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Example

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Here is how the Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered equation looks like with Values.

Here is how the Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered equation looks like with Units.

Here is how the Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered equation looks like.

0.604 = \frac{60 \cdot \tan (25) \cdot 0.06}{53 \cdot \tan (25 + 12.5) \cdot 0.06 + 0.16 \cdot 53 \cdot 0.04}

0.604 = \frac{60kg \cdot \tan (25°) \cdot 0.06m}{53N \cdot \tan (25° + 12.5°) \cdot 0.06m + 0.16 \cdot 53N \cdot 0.04m}

0.604 = \frac{60 \cdot \tan (25) \cdot 0.06}{53 \cdot \tan (25 + 12.5) \cdot 0.06 + 0.16 \cdot 53 \cdot 0.04}

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Home » Physics » Mechanical » Theory of Machine » Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered

Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Solution

Follow our step by step solution on how to calculate Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered?

FIRST Step Consider the formula

η = \frac{W \cdot \tan (ψ) \cdot d}{W l \cdot \tan (ψ + Φ) \cdot d + μ c \cdot W l \cdot R c}

Next Step Substitute values of Variables

∴

η = \frac{60kg \cdot \tan (25°) \cdot 0.06m}{53N \cdot \tan (25° + 12.5°) \cdot 0.06m + 0.16 \cdot 53N \cdot 0.04m}

Next Step Convert Units

∴

η = \frac{60kg \cdot \tan (0.4363rad) \cdot 0.06m}{53N \cdot \tan (0.4363rad + 0.2182rad) \cdot 0.06m + 0.16 \cdot 53N \cdot 0.04m}

Next Step Prepare to Evaluate

∴

η = \frac{60 \cdot \tan (0.4363) \cdot 0.06}{53 \cdot \tan (0.4363 + 0.2182) \cdot 0.06 + 0.16 \cdot 53 \cdot 0.04}

Next Step Evaluate

∴

η = 0.604003769657012

LAST Step Rounding Answer

∴

η = 0.604

Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Formula Elements

Variables

Functions

Efficiency

The Efficiency of an electric motor is defined as the ratio of usable shaft power to electric input power.

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Weight

Weight is a body's relative mass or the quantity of matter contained by it.

Symbol: W

Measurement: WeightUnit: kg

Note: Value can be positive or negative.

Helix Angle

Helix Angle is the angle between any helix and an axial line on its right, circular cylinder, or cone.

Symbol: ψ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Mean Diameter of Screw

Mean diameter of Screw is the distance from the outer thread on one side to the outer thread on the other side.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Load

Load is the weight of body lifted by screw jack.

Symbol: W_l

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Limiting Angle of Friction

The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be less than 90.

Coefficient of Friction For Collar

Coefficient of Friction For Collar is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.

Symbol: μ_c

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Mean Radius of Collar

Mean Radius of Collar is the mean of inner and outer radius of collar.

Symbol: R_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Formula and 2000+ more formulas!

Verified by Team Softusvista

Softusvista Office (Pune), India

Team Softusvista has verified this Formula and 1100+ more formulas!

Other Formulas to find Efficiency

Go Efficiency of Screw Jack when only Screw Friction is Considered

η = \frac{\tan (ψ)}{\tan (ψ + Φ)}

Go Maximum Efficiency of Screw Jack

η = \frac{1 - \sin (Φ)}{1 + \sin (Φ)}

Other formulas in Screw Jack category

Go Force Required to Lower Load by Screw Jack given Weight of Load

F = W l \cdot \frac{μ f \cdot \cos (ψ) - \sin (ψ)}{\cos (ψ) + μ f \cdot \sin (ψ)}

Go Force Required to Lower Load by Screw Jack given weight of load and Limiting angle

F = W l \cdot \tan (Φ - ψ)

How to Evaluate Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered?

Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered evaluator uses Efficiency = (Weight*tan(Helix Angle)*Mean Diameter of Screw)/(Load*tan(Helix Angle+Limiting Angle of Friction)*Mean Diameter of Screw+Coefficient of Friction For Collar*Load*Mean Radius of Collar) to evaluate the Efficiency, Efficiency of screw jack when screw friction as well as collar friction considered is the quality or degree of being efficient. Efficiency is denoted by η symbol.

How to evaluate Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered using this online evaluator? To use this online evaluator for Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered, enter Weight (W), Helix Angle (ψ), Mean Diameter of Screw (d), Load (W_l), Limiting Angle of Friction (Φ), Coefficient of Friction For Collar (μ_c) & Mean Radius of Collar (R_c) and hit the calculate button.

FAQs on Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered

What is the formula to find Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered?

The formula of Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered is expressed as Efficiency = (Weight*tan(Helix Angle)*Mean Diameter of Screw)/(Load*tan(Helix Angle+Limiting Angle of Friction)*Mean Diameter of Screw+Coefficient of Friction For Collar*Load*Mean Radius of Collar). Here is an example- 0.643257 = (60*tan(0.4363323129985)*0.06)/(53*tan(0.4363323129985+0.21816615649925)*0.06+0.16*53*0.04).

How to calculate Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered?

With Weight (W), Helix Angle (ψ), Mean Diameter of Screw (d), Load (W_l), Limiting Angle of Friction (Φ), Coefficient of Friction For Collar (μ_c) & Mean Radius of Collar (R_c) we can find Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered using the formula - Efficiency = (Weight*tan(Helix Angle)*Mean Diameter of Screw)/(Load*tan(Helix Angle+Limiting Angle of Friction)*Mean Diameter of Screw+Coefficient of Friction For Collar*Load*Mean Radius of Collar). This formula also uses Tangent (tan) function(s).

What are the other ways to Calculate Efficiency?

Here are the different ways to Calculate Efficiency-

Efficiency=tan(Helix Angle)/tan(Helix Angle+Limiting Angle of Friction)
Efficiency=(1-sin(Limiting Angle of Friction))/(1+sin(Limiting Angle of Friction))

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Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Formula

​GoEfficiency of Screw Jack when only Screw Friction is Considered Formula

​GoMaximum Efficiency of Screw Jack Formula

Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Example

Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Solution

Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered Formula Elements

Credits

Other Formulas to find Efficiency

Other formulas in Screw Jack category

How to Evaluate Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered?

FAQs on Efficiency of Screw Jack when Screw Friction as well as Collar Friction Considered

Variable Name

GoEfficiency of Screw Jack when only Screw Friction is Considered Formula

GoMaximum Efficiency of Screw Jack Formula